 Hello and welcome to the session. My name is Asha and I am going to help you with the following question that says integrate the following function 7.3x upon 1 plus 2x raised to the power 4. So first let us learn a formula to integrate a function of the form 1 upon x square plus a square with respect to x. So we equal to 1 upon a into tan inverse x upon a plus a. So with the help of this formula we are going to integrate the given function. So this is our t idea. Let us now start with the solution. Here the given function is 3x upon 1 plus 2x raised to the power 4. How we have to integrate this function with respect to x? Therefore we have integral 3x upon 1 plus 2x raised to the power 4 into dx. This can further be written as integral 3x dot dx upon 1 square plus root 2 into x square whole square. Now let us put root 2x square is equal to t. So this implies 2 root 2x into dx is equal to dt by differentiating both sides with respect to x we get this. Or x dot dx is equal to dt upon 2 root 2. Thus this expression can further be written as integral 3 into in place of dx we have sorry x dx we have dt upon 2 root 2 and we have 1 square plus this we have put as t. So we have t square. This is further equal to taking the constant outside the integral sign we have 3 upon 2 root 2 integral dt upon t square plus 1 square which is in the form of integral 1 upon x square plus a square into dx. Where in place of x we have t and in place of a we have 1. So this can further be written as 3 upon 2 root 2 into 1 upon 1 tan inverse t upon 1 plus c. This is with the help of key idea right. Now let us put the value of t. So we have 3 upon 2 root 2 into tan inverse root 2x square plus c. Thus on integrating the given function we get 3 upon 2 root 2 tan inverse root 2x square plus c. So this is our answer. This completes the session. Hope you have understood it. Take care and have a good day.